Transverse Spin Structure Research Articles

Exploring the spin structure of the nucleon at STAR

Understanding the internal spin structure of the nucleon remains a challenge in strong interaction physics. The unique capability of RHIC opened new avenues in studying the internal structure of the proton with unprecedented depth and precision. Significant progress has been made in the last few years through various measurements at STAR. The longitudinal spin measurements have contributed significantly to our understanding of the quark and gluon helicity distributions inside the proton. The longitudinal double-spin asymmetry, ALL, from STAR inclusive jet and dijet measurements provides the first evidence of a positive gluon polarization with partonic momentum fraction x > 0.05. The reconstruction of W±/Z in longitudinally polarized proton-proton collisions indicates that there is a flavor separation of the light sea quark helicity distributions. In transversely polarized proton collisions, W±/Z-bosons provide the first constraint on the sea-quark Sivers function and contributes to the tests of the predicted sign change. The tilt of the dijet opening angle provides a direct access to the first Mellin momentum of the Sivers function and avoids the spin-correlated fragmentation contributions. The novel measurements of the azimuthal distributions of identified hadrons in jets and spin-dependent dihadron correlations directly probe the collinear quark transversity in the proton, with the former coupled to the transverse momentum dependent (TMD) Collins fragmentation function and the latter to the dihadron interference fragmentation function. These measurements shed lights on Sivers function, quark transversity and spin-dependent fragmentation functions in both collinear and TMD formalism. In this proceeding, recent jet results on both the longitudinal and transverse spin structure of the proton from STAR are presented.

Improved room-temperature magnetoelectric coupling properties for multiferroic Z-type hexaferrites

Here we present the results of a systematic investigation of the effect of Ba substitution on the spiral magnetic structure and magnetoelectric effect in polycrystalline BaxSr3−xCo2Fe24O41 (x = 0.0, 0.1, 0.3, 0.5, and 0.7). The magnetoelectric coupling coefficient was improved from 455 ps/m (x = 0.0) to 624 ps/m (x = 0.3). Furthermore, the magnetic field range at which the magnetoelectric signal appears extended from 0-∼0.4 T (x = 0.0) to 0-∼0.9 T (x = 0.5), demonstrating that the transverse conical spin structure was significantly strengthened by Ba substitution. These improvements are attributed to the decrease of Fe-O-Fe bond angle near the L and S blocks boundary, the reduction of cone angle in the transverse conical spin structure, and the change in the distribution of magnetic Co ions caused by the substitution of large Ba ions for small Sr ions. In general, we achieved the improved magnetoelectric coupling strength in polycrystalline Z-type hexaferrite for the first time.

Collins and Sivers transverse-spin asymmetries in inclusive muoproduction of ρ0 mesons

The production of vector mesons in deep inelastic scattering is an interesting yet scarcely explored channel to study the transverse spin structure of the nucleon and the spin-dependence of fragmentation. The COMPASS collaboration has performed the first measurement of the Collins and Sivers asymmetries for inclusively produced ρ0 mesons. The analysis is based on the data set collected in deep inelastic scattering in 2010 using a 160GeV/cμ+ beam impinging on a transversely polarized NH3 target. The ρ0 mesons are selected from oppositely charged hadron pairs, and the asymmetries are extracted as a function of the Bjorken-x variable, the transverse momentum of the pair and the fraction of the energy z carried by the pair. Indications for positive Collins and Sivers asymmetries are observed.

Spinning gluons from the QCD light-ray OPE

We study the transverse spin structure of the squeezed limit of the three-point energy correlator, leftlangle mathrm{mathcal{E}}left({overrightarrow{n}}_1right)mathrm{mathcal{E}}left({overrightarrow{n}}_2right)mathrm{mathcal{E}}left({overrightarrow{n}}_3right)rightrangle . To describe its all orders perturbative behavior, we develop the light-ray operator product expansion (OPE) in QCD. At leading twist the iterated OPE of mathrm{mathcal{E}}left({overrightarrow{n}}_iright) operators closes onto light-ray operators {mathbbm{O}}^{left[Jright]}left(overrightarrow{n}right) with spin J, and transverse spin j = 0, 2. We compute the mathrm{mathcal{E}}left({overrightarrow{n}}_1right)mathrm{mathcal{E}}left({overrightarrow{n}}_2right) , mathrm{mathcal{E}}left({overrightarrow{n}}_1right){mathbbm{O}}^{left[Jright]}left({overrightarrow{n}}_2right) and {mathbbm{O}}^{left[{J}_1right]}left({overrightarrow{n}}_1right){mathbbm{O}}^{left[{J}_2right]}left({overrightarrow{n}}_2right) OPEs as analytic functions of J, which allows for the description of arbitrary squeezed limits of N -point correlators in QCD. We use these results with J = 3 to reproduce the perturbative expansion in the squeezed limit of the three-point correlator, as well as to resum the leading twist singular structure for both quark and gluon jets, including transverse spin contributions, as required for phenomenological applications. Finally, we briefly comment on the transverse spin structure at higher twists, and show that to all orders in the twist expansion the highest transverse spin contributions are universal between quark and gluon jets, and are descendants of the leading twist transverse spin-2 operator, allowing their resummation into a simple two-dimensional Euclidean conformal block. Due to the general applicability of our results to arbitrary correlation functions of energy flow operators, we anticipate that they can be widely applied to improving our understanding of jet substructure at the LHC.

Chiral magnetic structure of Y-type Ba0.6Sr1.4Zn2Fe12O22 hexaferrite in intermediate phase

Chiral magnetic structure of Y-type Ba0.6Sr1.4Zn2Fe12O22 hexaferrite in intermediate phase. / G. Khazaradze, A. Shengelaya. / Nano Studies. – 2020. – # 20. – pp. 131-136. – eng. Magnetic structure in intermediate-II and intermediate-III phases of Y-type hexaferrite single crystal Ba0.6Sr1.4Zn2Fe12O22 was investigated using neutron diffraction with polarization analysis. It was found that both phases have chiral magnetic structures. This shows that in contrast to previous assumptions, intermediate-II phase has transverse conical spin structure similar to the intermediate-III phase. Therefore, magnetic field induced ferroelectric state may exist also in the intermediate-II phase of Y-type Ba0.6Sr1.4Zn2Fe12O22 hexaferrite. Obtained results provide important insight into the recent observations of room temperature magnetoelectric coupling in Y-type Ba0.6Sr1.4Zn2Fe12O22 hexaferrite. Fig. 3, Ref. 12.

TMD observables in unpolarised Semi-Inclusive DIS at COMPASS

In 2016 and 2017, the COMPASS Collaboration at CERN collected a large sample of DIS events with a longitudinally polarised 160 GeV/c muon beam scattering off a liquid hydrogen target. Part of the collected data has been analysed to extract preliminary results for the amplitudes of the modulations in the azimuthal angle of the charged hadrons and for their transverse-momentum distributions. These observables give relevant information for the study of the transverse momentum and spin structure of the nucleon. Similarly to the results obtained in COMPASS with a deuteron target, the azimuthal asymmetries exhibit interesting kinematic dependences, while the squared-transverse-momentum distributions can be described by the sum of two exponential functions.

Measurement of Transverse Spin Dependent Azimuthal Correlations of Charged Pion(s) in $p^{\uparrow} p$ Collisions at $\sqrt s = 200$ GeV at STAR

At the leading twist, the transversity distribution function, h^{q}_{1}(x)h1q(x), where xx is the longitudinal momentum fraction of the proton carried by quark qq, encodes the transverse spin structure of the nucleon. Extraction of it is difficult because of its chiral-odd nature. In transversely polarized proton-proton collisions (p^\uparrow pp↑p), h_{1}^{q}(x)h1q(x) can be coupled with another chiral-odd partner, a spin-dependent fragmentation function (FF). The resulting asymmetries in hadron(s) azimuthal correlations directly probe h_{1}^{q}(x)h1q(x). We report the measurement of correlation asymmetries for charged pion(s) in p^\uparrow pp↑p, through the Collins and the Interference FF channel.

Measurement of Target Spin (in)dependent Asymmetries in Dimuon Production in Pion-Nucleon Collisions at COMPASS

The exploration of the transverse spin structure of the nucleon is one of the main topics of the COMPASS phase-II experiment. In 2015 and 2018 COMPASS performed Drell–Yan (DY) measurements using a 190 GeV \pmb{\pi^-}𝛑− beam interacting with a transversely polarized NH\pmb{_{3}}3 target and unpolarized W target. The azimuthal asymmetries in DY with transversely polarized NH_{3}3 target are sensitive to various transverse momentum dependent parton distribution functions. Preliminary results on the Sivers asymmetry are consistent with the QCD prediction for a sign-change of Sivers functions in DY. The angular coefficients \pmb{\lambda}𝛌, \pmb{\mu}𝛍 and \pmb{\nu}𝛎 that describe the unpolarized part of the DY cross section have been extracted from the data collected with W target. The preliminary results on the angular coefficients indicate the violation of the Lam–Tung relation, consistent with the observation in earlier DY experiments with pion beams.

Azimuthal asymmetries and transverse momentum distributions of charged hadrons in muon-proton deep inelastic scattering

In 2016 and 2017, the COMPASS Collaboration at CERN collected a large sample of DIS events with a longitudinally polarized 160 GeV/[Formula: see text] muon beam scattering off a liquid hydrogen target. Part of the collected data has been analyzed to extract preliminary results for the amplitudes of the modulations in the azimuthal angle of the charged hadrons and for their transverse momentum distributions. These observables give relevant information for the study of the transverse momentum and spin structure of the nucleon. The results, presented here for the first time, have been obtained from part of the data collected in 2016. In the analysis, a new method for the evaluation of the contribution of exclusive diffractive processes has been implemented. The azimuthal asymmetries exhibit strong kinematic dependencies, similar to those observed in COMPASS deuteron measurements. The transverse momentum distributions show smooth exponential trends and are compatible with the previous measurement on deuteron.

Transversity GPDs of the proton from lattice QCD

We present the first calculation of the $x$-dependence of the isovector transversity generalized parton distributions (GPDs) for the proton within lattice QCD. We compute the matrix elements with non-local operators containing a Wilson line. The calculation implements the Breit symmetric frame. The proton momenta are chosen as $0.83,\,1.25,\,1.67$ GeV, and the values of the momentum transfer squared are $0.69,\,1.02$ GeV$^2$. These combinations include cases with zero and nonzero skewness. The calculation is performed using one ensemble of two degenerate-mass light, a strange and a charm quark of maximally twisted mass fermions with a clover term. The lattice results are renormalized non-perturbatively and finally matched to the light-cone GPDs using one-loop perturbation theory within the framework of large momentum effective theory. The final GPDs are given in the $\overline{\rm MS}$ scheme at a scale of 2 GeV. In addition to the individual GPDs, we form the combination of the transversity GPDs that is related to the transverse spin structure of the proton. Finally, we extract the lowest two moments of GPDs and draw a number of important qualitative conclusions.

The large COMPASS polarized solid ammonia target for Drell–Yan measurements with a pion beam

The transversely polarized target (PT) of the COMPASS (NA58) collaboration at CERN has been used for Drell–Yan measurements in 2015 and 2018. The transverse spin structure of the proton has been studied using a negative pion beam and a solid ammonia target. Employing the dynamic nuclear polarization (DNP) method, proton polarization values of more than 80% have been routinely achieved after one day, at a homogeneous magnetic field of 2.5 T and using a 3He/4He dilution refrigerator. During the data-taking the target operates in a transversely oriented magnetic dipole field at 0.6 T. This so-called frozen spin operation mode without the DNP pumping process leads to a slow depolarization of the target material, which is further accelerated by the heat input of the pion beam, produced secondary particles and radiation damage effects to the target material. Ammonia has the highest resistance against radiation-induced depolarization among known solid target materials. The proton polarization has been measured by the nuclear magnetic resonance (NMR). Relaxation times of about 1100 h have been observed for the proton polarization resulting in an average polarization between 68% and 76% during about two weeks long data-taking periods. To achieve a systematic uncertainty of the polarization ΔP/P as low as 3.2% and a statistical one of less than 1.8% two large target cells with appropriate positioning of the NMR-coils have been built.

Dynamical spin excitations of the topological Haldane gapped phase in the S=1 Heisenberg antiferromagnetic chain with single-ion anisotropy

We study the dynamical spin excitations of the one-dimensional $S=1$ Heisenberg antiferromagnetic chain with single-ion anisotropy by using quantum Monte Carlo simulations and stochastic analytic continuation of imaginary-time correlation function. Using the transverse dynamic spin structure factor, we observe the quantum phase transition with a critical point between the topological Haldane gapped phase and the trivial phase. At the quantum critical point, we find a broad continuum characterized by the Tomonaga-Luttinger liquid similar to a $S=1/2$ Heisenberg antiferromagnetic chain. We further identify that the elementary excitations are fractionalized spinons.

Effect of dynamic sintering conditions on the room-temperature magnetoelectric response of multiferroic Sr3Co2Fe24O41

The effects of dynamic oxygen gas pressure during sintering on the room-temperature magnetoelectric effect (ME) of multiferroic Z-type hexaferrite Sr3Co2Fe24O41 were investigated for the first time. A maximum electrical resistivity of 2.78×109 Ω cm was obtained for samples sintered in a dynamic oxygen gas flow of 0.3 L/min. An important finding was that under high dynamic oxygen gas pressure during sintering a significantly broadening of the magnetic field range in which the ferroelectric phase state occurs was achieved. That is, the stability of the transverse conical spin structure is greatly enhanced by a high sintering oxygen gas pressure. Furthermore, the high sintering oxygen gas flow effectively decreases the leakage current and trapped states related to oxygen vacancies, stabilizing the ME and providing a more robust and unambiguous measurement of the magnetoelectric effect.

Room-temperature magnetoelectric effect in Al-doped Sr3Co2(Fe1-xAlx)24O41 hexaferrites

Here we present the results of a systematic investigation of the effect of Al doping on the room-temperature magnetoelectric properties of Z-type hexaferrites of the composition Sr3Co2(Fe1-xAlx)24O41 where x = 0, 0.02, 0.04, and 0.08. Aluminum doping is shown to stabilize the transverse conical spin structure and increase the range of magnetic fields in which the ferroelectric phase occurs for x ≤ 0.04. These characteristics are attributed to the favoring of the easy-axis magnetic anisotropy over the easy-plane brought about by Al doping. Furthermore, when x approaches 0.08, switching of the magnetic field leads to switching of the ferroelectric polarization, which is attributed to the transformation of the transverse conical spin structure into a new structure.

Magnetic structure factors Heisenberg model for magnetic ordered graphene like structure

We have theoretically studied the magnetic structure factors of Heisenberg model on honeycomb lattice in the presence of anisotropic Dzyaloshinskii–Moriya interaction and next nearest neighbor coupling exchange constant. A sublattice antiferromagnetic long range ordering has been considered for localized electrons on honeycomb lattice structure. In particular, the frequency dependence of both longitudinal and transverse dynamical spin susceptibilities has been investigated for various physical parameters in the model Hamiltonian. Using Holstein–Primakoff bosonic transformations, the behavior of magnetic susceptibilities properties has been studied by means of excitation spectrum of mapped bosonic gas. Furthermore we have studied the dependence of static spin susceptibilities on Dzyaloshinskii–Moriya interaction strength for various next nearest neighbor interaction strengths. We have found the dependence of static longitudinal spin structure factor on Dzyaloshinskii–Moriya interaction strength shows a divergence behavior at phase transition point for various next nearest neighbor exchange constants. Also our results show the position of peak in the dynamical transverse spin structure factor at fixed value for Dzyaloshinskii Moriya interaction moves to lower frequency with next nearest neighbor coupling constant.

Dynamical and static spin structure factors of Heisenberg antiferromagnet on honeycomb lattice in the presence of Dzyaloshinskii-Moriya interaction

We have theoretically studied the spin structure factors of Heisenberg model on honeycomb lattice in the presence of longitudinal magnetic field, i.e. magnetic field perpendicular to the honeycomb plane, and Dzyaloshinskii-Moriya interaction. The possible effects of next nearest neighbor exchange constant are investigated in terms of anisotropy in the Heisenberg interactions. This spatial anisotropy is due to the difference between nearest neighbor exchange coupling constant and next nearest neighbor exchange coupling constant. The original spin model hamiltonian is mapped to a bosonic model via a hard core bosonic transformation where an infinite hard core repulsion is imposed to constrain one boson occupation per site. Using Green's function approach, the energy spectrum of quasiparticle excitation has been obtained. The spectrum of the bosonic gas has been implemented in order to obtain two particle propagator which corresponds to spin structure factor of original Heisenberg chain model Hamiltonian. The results show the position of peak in the dynamical transverse spin structure factor at fixed value for Dzyaloshinskii Moriya interaction moves to higher frequency with magnetic field. Also the intensity of dynamical transverse spin structure factor is not affected by magnetic field. However the Dzyaloshinskii Moriya interaction strength causes to decrease the intensity of dynamical transverse spin structure factor. The increase of magnetic field does not varied the frequency position of peaks in dynamical longitudinal spin susceptibility however the intensity reduces with magnetic field. Our results show static transverse structure factor is found to be monotonically decreasing with magnetic field and temperature for different values of next nearest neighbor coupling exchange constant.

Magnetoelectricity in multiferroic hexaferrites as understood by crystal symmetry analyses

Magnetoelectric (ME) properties under rotating magnetic field H are comparatively investigated in two representative hexaferrites Y-type Ba0.5Sr1.5Zn2(Fe0.92Al0.08)12O22 and Z-type Ba0.52Sr2.48Co2Fe24O41, both of which have exhibited a similar transverse conical spin structure and giant ME coupling near room temperature. When the external H is rotated clockwise by 2pi, in-plane P vector is rotated clockwise by 2pi in the Y-type hexaferrite and counterclockwise by 4pi in the Z-type hexaferrite. A symmetry-based analysis reveals that the faster and opposite rotation of P vector in the Z-type hexaferrite is associated with the existence of a mirror plane perpendicular to c-axis. Moreover, such a peculiar crystal symmetry also results in contrasting microscopic origins for the spin-driven ferroelectricity; only the inverse DM interaction is responsible for the Y-type hexaferrite while additional p-d hybridization becomes more important in the Z-type hexaferrite. This work demonstrates the importance of the crystal symmetry in the determination of ME properties in the hexaferrites and provides a fundamental framework for understanding and applying the giant ME coupling in various ferrites with hexagonal crystal structure.

Suppression of Walker breakdown in gapped magnetic nanowires

We report a numerical study on the efficient and controllable suppression of the Walker breakdown along nanowires by positioning nanogaps with periodicity matching to that of transformational spin structure of the magnetic domain wall. While the Walker breakdown is suppressed, the transverse spin structure is found to be stably maintained without the formation of antivortex core throughout the propagation, shedding a light in faster spintronic devices based on the domain wall motion.

Observation of magnetic domain and bubble structures in magnetoelectric Sr3Co2Fe24O41

The magnetic domain and bubble structures in the Z-type hexaferrite Sr$_3$Co$_2$Fe$_{24}$O$_{41}$ were investigated using Lorentz microscopy. This hexaferrite exhibits a room-temperature magnetoelectric effect that is attributed to its transverse conical spin structure (TC phase). Upon heating, the TC phase transforms into a ferrimagnetic phase with magnetic moments in the hexagonal $ab$ plane between 410 and 480 K (FM2 phase) and into another ferrimagnetic phase with moments parallel to the $c$ axis between 490 and 680 K (FM1 phase). Accordingly, in this study, the magnetic domain structures in Sr$_3$Co$_2$Fe$_{24}$O$_{41}$ were observed to change dramatically with temperature. In the TC phase, irregular fine magnetic domains were observed after cooling the specimen from the FM2 to TC phase. In the FM1 phase, striped magnetic domain walls with pairs of bright and dark contrast were formed parallel to the $c$ axis. Upon applying an external magnetic field, the striped magnetic domain walls transformed into magnetic bubbles. The topology of the magnetic bubbles was dependent on the angle between the external magnetic field ($H$) direction and the easy $c$ axis. Namely, magnetic bubbles with the topological number $N$ = 1 (type I) were created for $H//c$, whereas magnetic bubbles with $N$ = 0 (type II) were created when the magnetic field was tilted from the c axis by 5{\deg}. We attribute the high magnetocrystalline anisotropy of Sr$_3$Co$_2$Fe$_{24}$O$_{41}$ to the emergence of magnetic bubbles in the FM1 phase.

Fermionic Hubbard model with Rashba or Dresselhaus spin–orbit coupling

In this work, we investigate the possible dramatic effects of Rashba or Dresselhaus spin–orbit coupling (SOC) on the fermionic Hubbard model in a two-dimensional square lattice. In the strong coupling limit, it leads to the rotated antiferromagnetic Heisenberg model which is a new class of quantum spin model. For a special equivalent class, we identify a new spin–orbital entangled commensurate ground (Y-y) state subject to strong quantum fluctuations at T = 0. We evaluate the quantum fluctuations by the spin wave expansion up to order . In some SOC parameter regimes, the Y-y state supports a massive relativistic incommensurate magnon (C-IC) with its two gap minima positions continuously tuned by the SOC parameters. The C-IC magnons dominate all the low temperature thermodynamic quantities and also lead to the separation of the peak positions between the longitudinal and the transverse spin structure factors. In the weak coupling limit, any weak repulsive interaction also leads to a weak Y-y state. There is only a crossover from the weak to the strong coupling. High temperature expansions of the specific heats in both weak and strong coupling are presented. The dramatic roles to be played by these C-IC magnons at generic SOC parameters or under various external probes are hinted at. Experimental applications to both layered noncentrosymmetric materials and cold atoms are discussed.